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JEE Main202225 Jun 2022Evening ShiftMathematicsVector AlgebraActual

Let b → = i ^ + j ^ + λ k ^ , λ ∈ ℝ . If a → is a vector such that a → × b → = 13 i ^ - j ^ - 4 k ^ and a → · b → + 21 = 0 , then b → - a → · k ^ - j ^ + b → + a → · i ^ - k ^ is equal to

Correct answer

0

Step-by-step solution

Let a → = x i ^ + y j ^ + z k ^ So, i ^ j ^ k ^ x y z 1 1 λ = i ^ λ y - z + j ^ z - λ x + k ^ x - y On comparing with 13 i ^ - j ^ - 4 k ^ we get, ⇒ λ y - z = 13 , z - λ x = - 1 , x - y = - 4 and x + y + λ z = - 21 ⇒ Clearly, λ = 3 , x = - 2 , y = 2 and z = - 7 So, b → - a → = 3 i ^ - j ^ + 10 k ^ and b → + a → = - i ^ + 3 j ^ - 4 k ^ ⇒ b → - a → · k ^ - j ^ + b → + a → · i ^ - k ^ = 11 + 3 = 14

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